Algorithm  is used to convert the spa-st instance \(I\)  in Figure REF  to an instance \(I^{\prime }\)  of HRT in Figure REF  which is then itself converted to the instance \(I^{\prime \prime }\)  of SMTI in Figure REF  using the process described by Manlove [1]}. In this process men correspond to hospitals in \(I^{\prime }\)  (projects in \(I\) ) and women correspond to residents in \(I^{\prime }\)  (students in \(I\) ). Executing Király's [2]} \(3/2\) -approximation algorithm on the smti instance \(I^{\prime \prime }\)  could (depending on order of proposals) yield the matching
\(M^{\prime \prime }=\lbrace (w_2,m_4), (w_4,m_3), (w_5,m_2), (w_6,m_6), (w_7,m_7)\rbrace \) 
